NOUREDDINE Benhamidouche

Djemiat Rabah

Etude de quelques modèles d'EDPS fractionnaires et leurs applications.

Arioua Oum Banine

Burgers equation and it’s applications

CHIKH Bochra

Etude d’un modéle mathématique liés à COVID 19

Hamza Guendouz

Équation de convection non linéaire et application

DJEDILI Rima

Les solutions de viscosit´ e des ´ equations aux d´ eriv´ ees partielles

Basti Bilal

Existence et unicité de solutions auto-similaires pour certaines équations fractionnaires non-linéaires

Basti Bilal

Existence et unicité de solutions auto-similaires pour certaines équations fractionnaires

Djaija Rami

EDPs et morphomogie mathématique

Lachache Mohamed

Etude d'existence et d'unicité de la solution du modèle de Caté et al

khenous amina

solutions auto similaires pour EDPs d'évoution fractionnaire

Choude Rafaa

Auto similarité et contour d'image

Chouder Rafaa

Auto similarité et contour d'image

Khechab Sara

classes de solutions pour le modèle de Pérona Malik unidimensionel

Ouadah asma , Redjem aicha

Quelques modèles mathématiques pour l'amélioration de contour d'image

Sadam Zerouak , Khaldoune Mohamed

Calcul fractionnaire et detection de contour d'image

Kouidri Nadia , Chicouche Imane

Sur les problèmes d'évolution à frontière libre

Bourahla houda , Rabhi chaima

Matlab pour traitement de l'image fondement et aplication

Benmehdi Sabah

Estimation bayesienn de l'exposant de Hurst

Dehimi Hayat

Etude mathématique et numérique de contour d'image par EDPs

Bisker Maroua

Etude du modèle non linéaire de Pérona Malik unidimensionel en traitement de l'image

Zourig Amel

EDPs et restauration d'image

Zenat Nassira

Restauration d'image de documents anciens

Arioua Yacine

Existence globale et explosion des solutions d'équation de réaction diffusion approche ondelette

Hannache Abdalah

Méthodes auto-similaires pour EDPs, Etude comparative

Refice Ahmed

Problème d’explosion de la solution d’équation de Type extension de Fujita par la méthode des ondelettes mobiles

Benkherrouche Amar

Etude de l’équation de Ginzburg- Landau par la méthode des ondelettes

Guelati Zineb

Etude de l’explosion de la solution l’équation de la Chaleur non-linéaire par la méthode des ondelettes mobiles

Arioua Yacine

Etude de l’équation de Fujita par la méthode des ondelettes mobiles

Chaker Mourad

Analyse par ondelettes en traitement du signal

Benmehdi Sabah

Etude du système réaction diffusion par la méthode des ondelettes mobiles

Aib Aziza

Instabilité gravitationnelle et ondelettes mobiles, cas deux ondelettes immobiles

In this paper, we shall study the existence and uniqueness of solutions called "traveling profiles solutions" to the porous medium equation in one dimension. By these solutions, we generalize the results obtained by Gilding and Peletier who proved the existence of self similar solutions of type I, II and III to the same equation. The principal idea of our work is to convert the porous media equation in to an equivalent nonlinear differential equation, and to prove the existence and uniqueness of these new solutions under certain conditions.

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2023-12-21), Existence of Traveling Profiles Solutions to Porous Medium Equation, Journal officiel Mathematics and Application, Vol:46, Issue:1, pages:149-162, Publishing House of Rzeszów University of Technology P.O. Box 85, 35-959 Rzeszów, Poland

Nous présentons le role des mathématiques dans le developpment dedivers domaine technolgiques notamment en industrie en en economie

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Noureddine BENHAMIDOUCHE , ,(2023-10-25), les mathématiques et les enjeux du developpment technologique,Mathematics and society,U.Msila - ENS Boussada

Nous présentons quelques aspects et exemples de modélisation mathématiques dans divers domaine technolgique s

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Noureddine BENHAMIDOUCHE , ,(2023-10-15), La modélisation mathématique aux service du developpment technologique,National conference on mathematics and applications,Université de Setif

This paper discusses and theoretically studies the existence and uniqueness of radially symmetric solutions for a multidimensional nonlinear time and space-fractional reaction-diffusion/wave equation that enables treating vibration and control, signal and image processing, and modeling earthquakes, among other physical phenomena. Additionally, application of Schauder’s and Banach’s fixed point theorems facilitates identifying the existence and uniqueness of solutions for the selected equation. The applicability of our main results is demonstrated through examples and explicit solutions.

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Noureddine BENHAMIDOUCHE , , (2023-05-06), THEORETICAL STUDIES ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A MULTIDIMENSIONAL NONLINEAR TIME AND SPACE-FRACTIONAL REACTION-DIFFUSION/WAVE EQUATION, Memoirs on Differential Equations and Mathematical Physics, Vol:89, Issue:2023, pages:1-16, Razmadze Mathematical Institute.

In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity vari- able η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Ouagueni Nora, , (2023-04-03), Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative, Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Vol:22, Issue:1, pages:49-74, Sciendo

This paper particularly addresses and discusses some analytical studies on the existence and uniqueness of global or blow-up solutions under the traveling profile forms for a free boundary problem of two-dimensional diffusion equations of moving fractional order. It does so by applying the properties of Schauder's and Banach's fixed point theorems. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.

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Noureddine BENHAMIDOUCHE , Rabah Djemiat, Basti Bilal, , (2022), Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order, Advances in the Theory of Nonlinear Analysis and its Application,, Vol:6, Issue:3, pages:287 - 299, e-ISSN: 2587-2648 Founded: 2017 Period: Quarterly Publisher: Erdal KARAPINAR

The fractional wave equation of higher order is presented as a generalization of the higher-order wave equation when arbitrary fractional-order derivatives are involved. This paper investigates the problem of existence and uniqueness of solutions under the traveling wave forms for a free boundary problem of higher-order space-fractional wave equations. It does so by applying the properties of Schauderís and Banachís Öxed point theorems

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Noureddine BENHAMIDOUCHE , Rabah Djemiat, Basti Bilal, , (2022), Existence Of Traveling Wave Solutions For A Free Boundary Problem Of Higher-Order Space-Fractional Wave Equations, Applied Mathematics E-Notes,, Vol:22, Issue:22, pages:427-436, http://www.math.nthu.edu.tw/amen

La conference traite les principes de la modélisation mathématique en biologie Elle traite les phénomènes d'épidimiologie etc;...

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Noureddine BENHAMIDOUCHE , ,(2022), Sur la modélisation mathématique en Biologie,Journnée Modélisation Mathématique en biologie,Universite de msila

The nonlinear diffusion equation is used to analyze the process of edge enhancement in image processing, based on a singularity principal, we study the image intensity evolution in the boundary layers around the edges of image. forms.

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Noureddine BENHAMIDOUCHE , ,(2021), Singularités et contours,Journnée International de Mathématiques, SMA 2021.,Alger

This paper investigates the problem of existence and uniqueness of solutions under the self-similar forms to the space-fractional heat equation. By applying the properties of Banach’s fixed point theorems, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type, we establish several results on the existence and uniqueness of self-similar solutions to this equation.

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Noureddine BENHAMIDOUCHE , bilal basti, , (2020), Existence results of self similar solutions to the caputo-types space-fractional heat equation, surveys in Mathematics and its applications, Vol:15, Issue:15, pages:153-168, http:/www.utgjiu.ro/math/sma

This work studies the existence and uniqueness of solutions for a class of nonlinear fractional di erential equations via the Katugampola fractional derivatives with an integral condition. The arguments for the study are based upon the Banach contraction principle, Schauder's xed point theorem, and the nonlinear alternative of Leray-Schauder type.

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Noureddine BENHAMIDOUCHE , Djemiat rabah, Basti Bilal, , (2020), Existence Results for Nonlinear Katugampola Fractional Differential Equations with an Integral Condition, Acta Math. Univ. Comenianae, Vol:89, Issue:2, pages:243-260, http://www.math.nthu.edu.tw/amen/

This paper investigates the problem of existence and uniqueness of positive solutions under the general self-similar form of the degenerate parabolic partial di§erential equation which is known as "nonlinear di§usion equation not in divergence form". By applying the properties of Banachís Öxed point theorems, we establish several results on the existence and uniqueness of the general form of self-similar solutions of this equation.

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Noureddine BENHAMIDOUCHE , Basti Bilal, , (2020), Global Existence and Blow-up of Generalized Self-Similar Solutions to Nonlinear Degenerate Diffusion Equation Not in Divergence Form, Applied Mathematics E-Notes,, Vol:20, Issue:20, pages:367-387, http://www.math.nthu.edu.tw/amen/

This work studies the existence and uniqueness of solutions for a class of nonlinear implicit fractional differential equations via the Katugampola fractional derivatives with an initial condition. The arguments for the study are based upon the Banach contraction principle, Schauders fixed point theorem and the nonlinear alternative of Leray-Schauder type

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Basti bilal, , (2019), Initial Value Problem For Nonlinear Implicit Fractional Differential Equations With Katugampola, Applied Mathematics E-Notes, Vol:19, Issue:19, pages:397-412, Tsing Hua University Hsinchu, TAIWAN

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach xed point theo- rems. For applications purposes, some examples are provided to demon- strate the usefulness of our main results.

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YACINE Arioua , Noureddine BENHAMIDOUCHE , Basti Bilal, , (2019), Existence and Uniqueness of Solutions for Nonlinear Katugampola Fractional Differential Equations, Journal of Mathematics and Applications, Vol:42, Issue:42, pages:35-61, Publishing House of Rzeszow University of Technology, Poland

In this paper, we would like to seek the new exact solutions to nonlinear diffusion equation that occurs in image processing. This equation is called degenerate parabolic equation. The solutions which we seek are called 'travelling profiles solutions'. For that, we have used the 'travelling profiles method' in order to find, explicitly, new exact solutions to this equation under some conditions. An interesting particular case has been discussed, this case coincides with particular solutions called 'intermediate asymptotic solutions' used to study the contour

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Noureddine BENHAMIDOUCHE , Chouder Rafaa, , (2019), New exact solutions to nonlinear diffusion equation that occurs in image processing, International Journal of Computing Science and Mathematics, Vol:10, Issue:4, pages:364 - 374, IJCSM - Inderscience Publishers

on présente une étude sur les modèles d'EDPS modélisant l’amélioration de contour d'image , avec des exemples d'illustration. en générale es problèmes sont mal posé, on discutera également de ce problème

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Noureddine BENHAMIDOUCHE , ,(2019), Modèles mathématiques de contours d’image,la 9ème édition du colloque Tendances dans les Applications Mathématiques en Tunisie Algérie Maroc,Tlemcen

We propose in this work to find explicit exact solutions called travelling profile solutions to a nonlinear diffusion equation that occurs in image processing. Some of these explicit solutions are related with the phenomenon of contour enhancement in image processing. We present a generalization of the results obtained by Barenblatt to study the contour enhancement in image processing for exponent range of parameter enhancement.

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Noureddine BENHAMIDOUCHE , Chouder Rafaa, , (2018), Travelling profile solutions for nonlinear degenerate parabolic equation and contour enhancement in image processing, Appl. Math. E-Notes, Vol:18, Issue:18, pages:1-12, Official Website http://www.math.nthu.edu.tw/~amen/

The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii’s fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2017), BOUNDARY VALUE PROBLEM FOR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS, Surveys in Mathematics and its Applications, Vol:12, Issue:12, pages:103-115, Bucharest University, Romania

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

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Noureddine BENHAMIDOUCHE , Benmehdi Sabah, N. Makarava, , (2011), Bayesian estimation of the self-similarity exponent of the Nile River, Nonlinear Processes in Geophysics, Vol:18, Issue:18, pages:441–446, EGU

We propose in this paper a new approach to construct exact solutions of nonlinear PDEs. The method used is called ”the travelling profiles method”. The travelling profiles method enables us to obtain many exact solutions to large classes of nonlinear PDEs

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YACINE Arioua , Noureddine BENHAMIDOUCHE , , (2009), New Method for Constructing Exact Solutions to Nonlinear PDEs, International Journal of Nonlinear Science, Vol:7, Issue:4, pages:395-398, World Academic Press, World Academic Union, England, UK

We suggest finding exact solutions of equation: \begin{equation*} \frac{\partial u}{\partial t}=(\frac{\partial ^{m}}{\partial x^{m}}u)^{p}, t\geq 0, x\in \mathbb{R}, m, p\in \mathbb{N}, p>1, \end{equation*} by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.

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Noureddine BENHAMIDOUCHE , , (2008), Exact solutions to some nonlinear PDEs, travelling profile method, Electronic Journal of Qualitative Theory of Differential Equations, Vol:15, Issue:15, pages:01-07, Bolyai Institute, University of Szeged and the Hungarian Academy of Sciences

We apply the travelling wavelets method to gravitational instability theory for the investigation of large-scale structure formation in cosmology. As the first step of our approach, the method is first applied to the 1D cosmological Euler-Poisson equation system. We test the stability of the linear (evolution) regime in this plane-symmetric case. As a result, our analysis confirms the existence of the linear regime for some configurations of fields describing the evolution of cosmological structures. Moreover, it provides us with estimates for the delay needed for structures of given scale and magnitude to deviate from the linear regime. We also exhibit other configurations for which the linear approximation is not valid at any time. In particular, density defaults (i.e. holes) turn out to be highly non-linear structures that dominate the evolution.

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Noureddine BENHAMIDOUCHE , Bruno Toresani, Roland Triay, , (1999), Traveling Wavelets approach to the Gravitational Instability theory, Monthly Notices of the Royal Astronomical Society, Vol:302, Issue:4, pages:807-820., Oxford Academic